Binary formally self-dual odd codes

Sunghyu Han; Heisook Lee; Yoonjin Lee

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Binary formally self-dual odd codes

机译：二进制形式的自对偶奇码

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摘要

Most of the research on formally self-dual (f'.s.d.) codes has been developed for binary f.s.d. even codes, but only limited research has been done for binary f.s.d. odd codes. In this article we complete the classification of binary f.s.d. odd codes of lengths up to 14. We also classify optimal binary f.s.d. odd codes of length 18 and 24, so our result completes the classification of binary optimal f.s.d. odd codes of lengths up to 26. For this classification we first find a relation between binary f.s.d. odd codes and binary f.s.d. even codes, and then we use this relation and the known classification results on binary f.s.d. even codes. We also classify (possibly) optimal binary double circulant f.s.d. odd codes of lengths up to 40.

机译：关于形式自对偶（f's.d。）代码的大多数研究都是针对二进制f.s.d开发的。即使是代码，但对二进制f.s.d的研究仅有限。奇数代码。在本文中，我们完成了二进制f.s.d的分类。奇数码的长度最大为14。我们还将最佳二进制f.s.d分类。奇数码的长度为18和24，因此我们的结果完成了二进制最优f.s.d的分类。奇数码的长度最大为26。对于这种分类，我们首先找到二进制f.s.d之间的关系。奇数代码和二进制f.s.d.偶数代码，然后我们使用此关系和二进制f.s.d上的已知分类结果。甚至代码。我们还对（可能）最佳二进制双循环f.s.d分类。长度不超过40的奇数代码。

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来源
《Designs, Codes and Crytography》 |2011年第2期|p.141-150|共10页
作者
Sunghyu Han; Heisook Lee; Yoonjin Lee;
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作者单位

School of Liberal Arts, Korea University of Technology and Education, Cheonan 330-708, Republic of Korea;

Department of Mathematics, Ewha Womans University, Seoul 120-750, Republic of Korea;

Department of Mathematics, Ewha Womans University, Seoul 120-750, Republic of Korea;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
formally; elf-dual; odes; ormally; elf-dual; ven; odes; ormally; elf-dual; dd; odes;

机译：正式地双偶颂歌正式地双偶ven颂歌正式地双偶dd;颂歌;

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专利

1. Binary formally self-dual odd codes [J] . Sunghyu Han, Heisook Lee, Yoonjin Lee Designs, Codes and Cryptography . 2011,第2期

机译：二进制形式的自对偶奇码
2. Classification of binary self-dual [48,24,10] codes with an automorphism of odd prime order [J] . Stefka Bouyuklieva, Nikolay Yankov, Jon-Lark Kim Finite fields and their applications . 2012,第6期

机译：具有奇素数阶自同构的二进制自对偶[48,24,10]码的分类
3. On the structure of binary self-dual codes having an automorphism of order a square of an odd prime [J] . Bouyuklieva S., Russeva R., Yankov N. IEEE Transactions on Information Theory . 2005,第10期

机译：关于具有奇素数平方的自同构的二进制自对偶码的结构
4. On the Formally Self-Dual Binary 30, 15, 8 Codes [C] . Stefka Bouyuklieva, Iliya Bouyukliev International Workshop on Algebraic and Combinatorial Coding Theory . 2020

机译：在正式自我二进制30,15,8代码上
5. Arithmetic constructions of binary self-dual codes. [D] . Zhang, Ying. 2013

机译：二进制自对偶码的算术构造。
6. Identifying Odd/Even-Order Binary Kernel Slices for a Nonlinear System Using Inverse Repeat m-Sequences [O] . Jin-yan Hu, Gang Yan, Tao Wang 2015

机译：使用反向重复m序列识别非线性系统的奇/偶数二进制核切片
7. Classification of binary self-dual 48,24,10 codes with an automorphism of odd prime order [O] . Bouyuklieva Stefka, Yankov Nikolay, Kim Jon-Lark 2012

机译：具有奇素数阶自同构的二进制自对偶48,24,10码的分类

Binary formally self-dual odd codes

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